RNA polymerase motors: dwell time distribution, velocity and dynamical phases

Polymerization of RNA from a template DNA is carried out by a molecular machine called RNA polymerase (RNAP). It also uses the template as a track on which it moves as a motor utilizing chemical energy input. The time it spends at each successive monomer of DNA is random; we derive the exact distribution of these “dwell times” in our model. The inverse of the mean dwell time satisfies a Michaelis-Menten-like equation and is also consistent with a general formula derived earlier by Fisher and Kolomeisky for molecular motors with unbranched mechano-chemical cycles. Often many RNAP motors move simultaneously on the same track. Incorporating the steric interactions among the RNAPs in our model, we also plot the three-dimensional phase diagram of our model for RNAP traffic using an extremum current hypothesis.

💡 Research Summary

The paper presents a comprehensive theoretical study of RNA polymerase (RNAP) dynamics, focusing on two complementary aspects: the stochastic dwell time of a single RNAP at each nucleotide of the DNA template, and the collective behavior of many RNAPs moving simultaneously along the same track.

Single‑molecule dwell‑time analysis
The authors model the transcription elongation cycle as an unbranched mechano‑chemical pathway consisting of two forward chemical transitions—NTP binding (rate k₁) and phosphodiester bond formation (rate k₂)—and their corresponding reverse rates (k₋₁, k₋₂). By treating the process as a continuous‑time Markov chain, they derive an exact expression for the probability density ψ(t) of the dwell time t. ψ(t) is a sum of two exponentials whose decay constants are the eigenvalues of the transition‑rate matrix. The mean dwell time ⟨τ⟩ follows directly from the rates, and its inverse, the average stepping velocity v = 1/⟨τ⟩, takes the Michaelis–Menten form

v = (V_max